Moreover, we pointed out that some non-topological edge states without the
protection of the chiral symmetry can be found in the gap within bulk bands
that are away from zero-energy (Fermi level). The existence and number of
these states are sensitive to the edge configurations of BLG ribbons even if
their bulk topologies are the same, which can be simply explained by
effective Hamiltonians \(H(k_{y}=\pi )\)  for different situations. Though we
focus only on the honeycomb lattice in this paper, it should be obvious that
our study can be generalized to lattices of different shapes, such as Kagome
[1]}, [2]} and triangular [3]} lattices, and of higher
dimensions, such as the description of edge states and surface states in
three dimensional topological insulators [4]}, [5]}. All of these
provide potential directions for further study.
